Hochschild homology of associative rings, first studied by Hochschild [1]} and Cartan-Eilenberg [2]}, generalizes the notion of Kähler differentials from the commutative to the merely associative setting. Hochschild homology is an important tool for non-commutative geometry [3]}, which satisfies interesting properties such as Morita invariance [4]} and which provides a useful approximation to algebraic \(K\) -theory via the Dennis trace [5]}, [6]}. The homotopical analogue of classical Hochschild homology, topological Hochschild homology (\(\mathrm {THH}\) ) of ring spectra, admits an analogous Dennis trace map from algebraic \(K\) -theory [7]}, [8]}.
